/*    $OpenBSD: tree.h,v 1.29 2017/07/30 19:27:20 deraadt Exp $    */
/*
 * Copyright 2002 Niels Provos <provos@citi.umich.edu>
 * All rights reserved.
 *
 * Redistribution and use in source and binary forms, with or without
 * modification, are permitted provided that the following conditions
 * are met:
 * 1. Redistributions of source code must retain the above copyright
 *    notice, this list of conditions and the following disclaimer.
 * 2. Redistributions in binary form must reproduce the above copyright
 *    notice, this list of conditions and the following disclaimer in the
 *    documentation and/or other materials provided with the distribution.
 *
 * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR
 * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
 * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
 * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT,
 * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
 * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
 * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
 * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
 * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
 * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
 */

#ifndef    _SYS_TREE_H_
#define    _SYS_TREE_H_

#include <sys/_null.h>

/*
 * This file defines data structures for different types of trees:
 * splay trees and red-black trees.
 *
 * A splay tree is a self-organizing data structure.  Every operation
 * on the tree causes a splay to happen.  The splay moves the requested
 * node to the root of the tree and partly rebalances it.
 *
 * This has the benefit that request locality causes faster lookups as
 * the requested nodes move to the top of the tree.  On the other hand,
 * every lookup causes memory writes.
 *
 * The Balance Theorem bounds the total access time for m operations
 * and n inserts on an initially empty tree as O((m + n)lg n).  The
 * amortized cost for a sequence of m accesses to a splay tree is O(lg n);
 *
 * A red-black tree is a binary search tree with the node color as an
 * extra attribute.  It fulfills a set of conditions:
 *    - every search path from the root to a leaf consists of the
 *      same number of black nodes,
 *    - each red node (except for the root) has a black parent,
 *    - each leaf node is black.
 *
 * Every operation on a red-black tree is bounded as O(lg n).
 * The maximum height of a red-black tree is 2lg (n+1).
 */

#define SPLAY_HEAD(name, type)                        \
struct name {                                \
struct type *sph_root; /* root of the tree */            \
}

#define SPLAY_INITIALIZER(root)                        \
{ NULL }

#define SPLAY_INIT(root) do {                        \
(root)->sph_root = NULL;                    \
} while (0)

#define SPLAY_ENTRY(type)                        \
struct {                                \
struct type *spe_left; /* left element */            \
struct type *spe_right; /* right element */            \
}

#define SPLAY_LEFT(elm, field)        (elm)->field.spe_left
#define SPLAY_RIGHT(elm, field)        (elm)->field.spe_right
#define SPLAY_ROOT(head)        (head)->sph_root
#define SPLAY_EMPTY(head)        (SPLAY_ROOT(head) == NULL)

/* SPLAY_ROTATE_{LEFT,RIGHT} expect that tmp hold SPLAY_{RIGHT,LEFT} */
#define SPLAY_ROTATE_RIGHT(head, tmp, field) do {            \
SPLAY_LEFT((head)->sph_root, field) = SPLAY_RIGHT(tmp, field);    \
SPLAY_RIGHT(tmp, field) = (head)->sph_root;            \
(head)->sph_root = tmp;                        \
} while (0)

#define SPLAY_ROTATE_LEFT(head, tmp, field) do {            \
SPLAY_RIGHT((head)->sph_root, field) = SPLAY_LEFT(tmp, field);    \
SPLAY_LEFT(tmp, field) = (head)->sph_root;            \
(head)->sph_root = tmp;                        \
} while (0)

#define SPLAY_LINKLEFT(head, tmp, field) do {                \
SPLAY_LEFT(tmp, field) = (head)->sph_root;            \
tmp = (head)->sph_root;                        \
(head)->sph_root = SPLAY_LEFT((head)->sph_root, field);        \
} while (0)

#define SPLAY_LINKRIGHT(head, tmp, field) do {                \
SPLAY_RIGHT(tmp, field) = (head)->sph_root;            \
tmp = (head)->sph_root;                        \
(head)->sph_root = SPLAY_RIGHT((head)->sph_root, field);    \
} while (0)

#define SPLAY_ASSEMBLE(head, node, left, right, field) do {        \
SPLAY_RIGHT(left, field) = SPLAY_LEFT((head)->sph_root, field);    \
SPLAY_LEFT(right, field) = SPLAY_RIGHT((head)->sph_root, field);\
SPLAY_LEFT((head)->sph_root, field) = SPLAY_RIGHT(node, field);    \
SPLAY_RIGHT((head)->sph_root, field) = SPLAY_LEFT(node, field);    \
} while (0)

/* Generates prototypes and inline functions */

#define SPLAY_PROTOTYPE(name, type, field, cmp)                \
void name##_SPLAY(struct name *, struct type *);            \
void name##_SPLAY_MINMAX(struct name *, int);                \
struct type *name##_SPLAY_INSERT(struct name *, struct type *);        \
struct type *name##_SPLAY_REMOVE(struct name *, struct type *);        \
\
/* Finds the node with the same key as elm */                \
static __unused __inline struct type *                    \
name##_SPLAY_FIND(struct name *head, struct type *elm)            \
{                                    \
if (SPLAY_EMPTY(head))                        \
return(NULL);                        \
name##_SPLAY(head, elm);                    \
if ((cmp)(elm, (head)->sph_root) == 0)                \
return (head->sph_root);                \
return (NULL);                            \
}                                    \
\
static __unused __inline struct type *                    \
name##_SPLAY_NEXT(struct name *head, struct type *elm)            \
{                                    \
name##_SPLAY(head, elm);                    \
if (SPLAY_RIGHT(elm, field) != NULL) {                \
elm = SPLAY_RIGHT(elm, field);                \
while (SPLAY_LEFT(elm, field) != NULL) {        \
elm = SPLAY_LEFT(elm, field);            \
}                            \
} else                                \
elm = NULL;                        \
return (elm);                            \
}                                    \
\
static __unused __inline struct type *                    \
name##_SPLAY_MIN_MAX(struct name *head, int val)            \
{                                    \
name##_SPLAY_MINMAX(head, val);                    \
return (SPLAY_ROOT(head));                    \
}

/* Main splay operation.
 * Moves node close to the key of elm to top
 */
#define SPLAY_GENERATE(name, type, field, cmp)                \
struct type *                                \
name##_SPLAY_INSERT(struct name *head, struct type *elm)        \
{                                    \
if (SPLAY_EMPTY(head)) {                        \
SPLAY_LEFT(elm, field) = SPLAY_RIGHT(elm, field) = NULL;    \
} else {                                \
int __comp;                            \
name##_SPLAY(head, elm);                    \
__comp = (cmp)(elm, (head)->sph_root);            \
if(__comp < 0) {                        \
SPLAY_LEFT(elm, field) = SPLAY_LEFT((head)->sph_root, field);\
SPLAY_RIGHT(elm, field) = (head)->sph_root;        \
SPLAY_LEFT((head)->sph_root, field) = NULL;        \
} else if (__comp > 0) {                    \
SPLAY_RIGHT(elm, field) = SPLAY_RIGHT((head)->sph_root, field);\
SPLAY_LEFT(elm, field) = (head)->sph_root;        \
SPLAY_RIGHT((head)->sph_root, field) = NULL;    \
} else                            \
return ((head)->sph_root);                \
}                                    \
(head)->sph_root = (elm);                        \
return (NULL);                            \
}                                    \
\
struct type *                                \
name##_SPLAY_REMOVE(struct name *head, struct type *elm)        \
{                                    \
struct type *__tmp;                        \
if (SPLAY_EMPTY(head))                        \
return (NULL);                        \
name##_SPLAY(head, elm);                    \
if ((cmp)(elm, (head)->sph_root) == 0) {            \
if (SPLAY_LEFT((head)->sph_root, field) == NULL) {    \
(head)->sph_root = SPLAY_RIGHT((head)->sph_root, field);\
} else {                        \
__tmp = SPLAY_RIGHT((head)->sph_root, field);    \
(head)->sph_root = SPLAY_LEFT((head)->sph_root, field);\
name##_SPLAY(head, elm);            \
SPLAY_RIGHT((head)->sph_root, field) = __tmp;    \
}                            \
return (elm);                        \
}                                \
return (NULL);                            \
}                                    \
\
void                                    \
name##_SPLAY(struct name *head, struct type *elm)            \
{                                    \
struct type __node, *__left, *__right, *__tmp;            \
int __comp;                            \
\
SPLAY_LEFT(&__node, field) = SPLAY_RIGHT(&__node, field) = NULL;\
__left = __right = &__node;                    \
\
while ((__comp = (cmp)(elm, (head)->sph_root))) {        \
if (__comp < 0) {                    \
__tmp = SPLAY_LEFT((head)->sph_root, field);    \
if (__tmp == NULL)                \
break;                    \
if ((cmp)(elm, __tmp) < 0){            \
SPLAY_ROTATE_RIGHT(head, __tmp, field);    \
if (SPLAY_LEFT((head)->sph_root, field) == NULL)\
break;                \
}                        \
SPLAY_LINKLEFT(head, __right, field);        \
} else if (__comp > 0) {                \
__tmp = SPLAY_RIGHT((head)->sph_root, field);    \
if (__tmp == NULL)                \
break;                    \
if ((cmp)(elm, __tmp) > 0){            \
SPLAY_ROTATE_LEFT(head, __tmp, field);    \
if (SPLAY_RIGHT((head)->sph_root, field) == NULL)\
break;                \
}                        \
SPLAY_LINKRIGHT(head, __left, field);        \
}                            \
}                                \
SPLAY_ASSEMBLE(head, &__node, __left, __right, field);        \
}                                    \
\
/* Splay with either the minimum or the maximum element            \
* Used to find minimum or maximum element in tree.            \
*/                                    \
void name##_SPLAY_MINMAX(struct name *head, int __comp) \
{                                    \
struct type __node, *__left, *__right, *__tmp;            \
\
SPLAY_LEFT(&__node, field) = SPLAY_RIGHT(&__node, field) = NULL;\
__left = __right = &__node;                    \
\
while (1) {                            \
if (__comp < 0) {                    \
__tmp = SPLAY_LEFT((head)->sph_root, field);    \
if (__tmp == NULL)                \
break;                    \
if (__comp < 0){                \
SPLAY_ROTATE_RIGHT(head, __tmp, field);    \
if (SPLAY_LEFT((head)->sph_root, field) == NULL)\
break;                \
}                        \
SPLAY_LINKLEFT(head, __right, field);        \
} else if (__comp > 0) {                \
__tmp = SPLAY_RIGHT((head)->sph_root, field);    \
if (__tmp == NULL)                \
break;                    \
if (__comp > 0) {                \
SPLAY_ROTATE_LEFT(head, __tmp, field);    \
if (SPLAY_RIGHT((head)->sph_root, field) == NULL)\
break;                \
}                        \
SPLAY_LINKRIGHT(head, __left, field);        \
}                            \
}                                \
SPLAY_ASSEMBLE(head, &__node, __left, __right, field);        \
}

#define SPLAY_NEGINF    -1
#define SPLAY_INF    1

#define SPLAY_INSERT(name, x, y)    name##_SPLAY_INSERT(x, y)
#define SPLAY_REMOVE(name, x, y)    name##_SPLAY_REMOVE(x, y)
#define SPLAY_FIND(name, x, y)        name##_SPLAY_FIND(x, y)
#define SPLAY_NEXT(name, x, y)        name##_SPLAY_NEXT(x, y)
#define SPLAY_MIN(name, x)        (SPLAY_EMPTY(x) ? NULL    \
: name##_SPLAY_MIN_MAX(x, SPLAY_NEGINF))
#define SPLAY_MAX(name, x)        (SPLAY_EMPTY(x) ? NULL    \
: name##_SPLAY_MIN_MAX(x, SPLAY_INF))

#define SPLAY_FOREACH(x, name, head)                    \
for ((x) = SPLAY_MIN(name, head);                \
(x) != NULL;                        \
(x) = SPLAY_NEXT(name, head, x))

/* Macros that define a red-black tree */
#define RB_HEAD(name, type)                        \
struct name {                                \
struct type *rbh_root; /* root of the tree */            \
}

#define RB_INITIALIZER(root)                        \
{ NULL }

#define RB_INIT(root) do {                        \
(root)->rbh_root = NULL;                    \
} while (0)

#define RB_BLACK    0
#define RB_RED        1
#define RB_ENTRY(type)                            \
struct {                                \
struct type *rbe_left;        /* left element */        \
struct type *rbe_right;        /* right element */        \
struct type *rbe_parent;    /* parent element */        \
int rbe_color;            /* node color */        \
}

#define RB_LEFT(elm, field)        (elm)->field.rbe_left
#define RB_RIGHT(elm, field)        (elm)->field.rbe_right
#define RB_PARENT(elm, field)        (elm)->field.rbe_parent
#define RB_COLOR(elm, field)        (elm)->field.rbe_color
#define RB_ROOT(head)            (head)->rbh_root
#define RB_EMPTY(head)            (RB_ROOT(head) == NULL)

#define RB_SET(elm, parent, field) do {                    \
RB_PARENT(elm, field) = parent;                    \
RB_LEFT(elm, field) = RB_RIGHT(elm, field) = NULL;        \
RB_COLOR(elm, field) = RB_RED;                    \
} while (0)

#define RB_SET_BLACKRED(black, red, field) do {                \
RB_COLOR(black, field) = RB_BLACK;                \
RB_COLOR(red, field) = RB_RED;                    \
} while (0)

#ifndef RB_AUGMENT
#define RB_AUGMENT(x)    do {} while (0)
#endif

#define RB_ROTATE_LEFT(head, elm, tmp, field) do {            \
(tmp) = RB_RIGHT(elm, field);                    \
if ((RB_RIGHT(elm, field) = RB_LEFT(tmp, field))) {        \
RB_PARENT(RB_LEFT(tmp, field), field) = (elm);        \
}                                \
RB_AUGMENT(elm);                        \
if ((RB_PARENT(tmp, field) = RB_PARENT(elm, field))) {        \
if ((elm) == RB_LEFT(RB_PARENT(elm, field), field))    \
RB_LEFT(RB_PARENT(elm, field), field) = (tmp);    \
else                            \
RB_RIGHT(RB_PARENT(elm, field), field) = (tmp);    \
} else                                \
(head)->rbh_root = (tmp);                \
RB_LEFT(tmp, field) = (elm);                    \
RB_PARENT(elm, field) = (tmp);                    \
RB_AUGMENT(tmp);                        \
if ((RB_PARENT(tmp, field)))                    \
RB_AUGMENT(RB_PARENT(tmp, field));            \
} while (0)

#define RB_ROTATE_RIGHT(head, elm, tmp, field) do {            \
(tmp) = RB_LEFT(elm, field);                    \
if ((RB_LEFT(elm, field) = RB_RIGHT(tmp, field))) {        \
RB_PARENT(RB_RIGHT(tmp, field), field) = (elm);        \
}                                \
RB_AUGMENT(elm);                        \
if ((RB_PARENT(tmp, field) = RB_PARENT(elm, field))) {        \
if ((elm) == RB_LEFT(RB_PARENT(elm, field), field))    \
RB_LEFT(RB_PARENT(elm, field), field) = (tmp);    \
else                            \
RB_RIGHT(RB_PARENT(elm, field), field) = (tmp);    \
} else                                \
(head)->rbh_root = (tmp);                \
RB_RIGHT(tmp, field) = (elm);                    \
RB_PARENT(elm, field) = (tmp);                    \
RB_AUGMENT(tmp);                        \
if ((RB_PARENT(tmp, field)))                    \
RB_AUGMENT(RB_PARENT(tmp, field));            \
} while (0)

/* Generates prototypes and inline functions */
#define    RB_PROTOTYPE(name, type, field, cmp)                \
RB_PROTOTYPE_INTERNAL(name, type, field, cmp,)
#define    RB_PROTOTYPE_STATIC(name, type, field, cmp)            \
RB_PROTOTYPE_INTERNAL(name, type, field, cmp, __attribute__((__unused__)) static)
#define RB_PROTOTYPE_INTERNAL(name, type, field, cmp, attr)        \
attr void name##_RB_INSERT_COLOR(struct name *, struct type *);        \
attr void name##_RB_REMOVE_COLOR(struct name *, struct type *, struct type *);\
attr struct type *name##_RB_REMOVE(struct name *, struct type *);    \
attr struct type *name##_RB_INSERT(struct name *, struct type *);    \
attr struct type *name##_RB_FIND(struct name *, struct type *);        \
attr struct type *name##_RB_NFIND(struct name *, struct type *);    \
attr struct type *name##_RB_NEXT(struct type *);            \
attr struct type *name##_RB_PREV(struct type *);            \
attr struct type *name##_RB_MINMAX(struct name *, int);            \
\

/* Main rb operation.
 * Moves node close to the key of elm to top
 */
#define    RB_GENERATE(name, type, field, cmp)                \
RB_GENERATE_INTERNAL(name, type, field, cmp,)
#define    RB_GENERATE_STATIC(name, type, field, cmp)            \
RB_GENERATE_INTERNAL(name, type, field, cmp, __attribute__((__unused__)) static)
#define RB_GENERATE_INTERNAL(name, type, field, cmp, attr)        \
attr void                                \
name##_RB_INSERT_COLOR(struct name *head, struct type *elm)        \
{                                    \
struct type *parent, *gparent, *tmp;                \
while ((parent = RB_PARENT(elm, field)) &&            \
RB_COLOR(parent, field) == RB_RED) {            \
gparent = RB_PARENT(parent, field);            \
if (parent == RB_LEFT(gparent, field)) {        \
tmp = RB_RIGHT(gparent, field);            \
if (tmp && RB_COLOR(tmp, field) == RB_RED) {    \
RB_COLOR(tmp, field) = RB_BLACK;    \
RB_SET_BLACKRED(parent, gparent, field);\
elm = gparent;                \
continue;                \
}                        \
if (RB_RIGHT(parent, field) == elm) {        \
RB_ROTATE_LEFT(head, parent, tmp, field);\
tmp = parent;                \
parent = elm;                \
elm = tmp;                \
}                        \
RB_SET_BLACKRED(parent, gparent, field);    \
RB_ROTATE_RIGHT(head, gparent, tmp, field);    \
} else {                        \
tmp = RB_LEFT(gparent, field);            \
if (tmp && RB_COLOR(tmp, field) == RB_RED) {    \
RB_COLOR(tmp, field) = RB_BLACK;    \
RB_SET_BLACKRED(parent, gparent, field);\
elm = gparent;                \
continue;                \
}                        \
if (RB_LEFT(parent, field) == elm) {        \
RB_ROTATE_RIGHT(head, parent, tmp, field);\
tmp = parent;                \
parent = elm;                \
elm = tmp;                \
}                        \
RB_SET_BLACKRED(parent, gparent, field);    \
RB_ROTATE_LEFT(head, gparent, tmp, field);    \
}                            \
}                                \
RB_COLOR(head->rbh_root, field) = RB_BLACK;            \
}                                    \
\
attr void                                \
name##_RB_REMOVE_COLOR(struct name *head, struct type *parent, struct type *elm) \
{                                    \
struct type *tmp;                        \
while ((elm == NULL || RB_COLOR(elm, field) == RB_BLACK) &&    \
elm != RB_ROOT(head)) {                    \
if (RB_LEFT(parent, field) == elm) {            \
tmp = RB_RIGHT(parent, field);            \
if (RB_COLOR(tmp, field) == RB_RED) {        \
RB_SET_BLACKRED(tmp, parent, field);    \
RB_ROTATE_LEFT(head, parent, tmp, field);\
tmp = RB_RIGHT(parent, field);        \
}                        \
if ((RB_LEFT(tmp, field) == NULL ||        \
RB_COLOR(RB_LEFT(tmp, field), field) == RB_BLACK) &&\
(RB_RIGHT(tmp, field) == NULL ||        \
RB_COLOR(RB_RIGHT(tmp, field), field) == RB_BLACK)) {\
RB_COLOR(tmp, field) = RB_RED;        \
elm = parent;                \
parent = RB_PARENT(elm, field);        \
} else {                    \
if (RB_RIGHT(tmp, field) == NULL ||    \
RB_COLOR(RB_RIGHT(tmp, field), field) == RB_BLACK) {\
struct type *oleft;        \
if ((oleft = RB_LEFT(tmp, field)))\
RB_COLOR(oleft, field) = RB_BLACK;\
RB_COLOR(tmp, field) = RB_RED;    \
RB_ROTATE_RIGHT(head, tmp, oleft, field);\
tmp = RB_RIGHT(parent, field);    \
}                    \
RB_COLOR(tmp, field) = RB_COLOR(parent, field);\
RB_COLOR(parent, field) = RB_BLACK;    \
if (RB_RIGHT(tmp, field))        \
RB_COLOR(RB_RIGHT(tmp, field), field) = RB_BLACK;\
RB_ROTATE_LEFT(head, parent, tmp, field);\
elm = RB_ROOT(head);            \
break;                    \
}                        \
} else {                        \
tmp = RB_LEFT(parent, field);            \
if (RB_COLOR(tmp, field) == RB_RED) {        \
RB_SET_BLACKRED(tmp, parent, field);    \
RB_ROTATE_RIGHT(head, parent, tmp, field);\
tmp = RB_LEFT(parent, field);        \
}                        \
if ((RB_LEFT(tmp, field) == NULL ||        \
RB_COLOR(RB_LEFT(tmp, field), field) == RB_BLACK) &&\
(RB_RIGHT(tmp, field) == NULL ||        \
RB_COLOR(RB_RIGHT(tmp, field), field) == RB_BLACK)) {\
RB_COLOR(tmp, field) = RB_RED;        \
elm = parent;                \
parent = RB_PARENT(elm, field);        \
} else {                    \
if (RB_LEFT(tmp, field) == NULL ||    \
RB_COLOR(RB_LEFT(tmp, field), field) == RB_BLACK) {\
struct type *oright;        \
if ((oright = RB_RIGHT(tmp, field)))\
RB_COLOR(oright, field) = RB_BLACK;\
RB_COLOR(tmp, field) = RB_RED;    \
RB_ROTATE_LEFT(head, tmp, oright, field);\
tmp = RB_LEFT(parent, field);    \
}                    \
RB_COLOR(tmp, field) = RB_COLOR(parent, field);\
RB_COLOR(parent, field) = RB_BLACK;    \
if (RB_LEFT(tmp, field))        \
RB_COLOR(RB_LEFT(tmp, field), field) = RB_BLACK;\
RB_ROTATE_RIGHT(head, parent, tmp, field);\
elm = RB_ROOT(head);            \
break;                    \
}                        \
}                            \
}                                \
if (elm)                            \
RB_COLOR(elm, field) = RB_BLACK;            \
}                                    \
\
attr struct type *                            \
name##_RB_REMOVE(struct name *head, struct type *elm)            \
{                                    \
struct type *child, *parent, *old = elm;            \
int color;                            \
if (RB_LEFT(elm, field) == NULL)                \
child = RB_RIGHT(elm, field);                \
else if (RB_RIGHT(elm, field) == NULL)                \
child = RB_LEFT(elm, field);                \
else {                                \
struct type *left;                    \
elm = RB_RIGHT(elm, field);                \
while ((left = RB_LEFT(elm, field)))            \
elm = left;                    \
child = RB_RIGHT(elm, field);                \
parent = RB_PARENT(elm, field);                \
color = RB_COLOR(elm, field);                \
if (child)                        \
RB_PARENT(child, field) = parent;        \
if (parent) {                        \
if (RB_LEFT(parent, field) == elm)        \
RB_LEFT(parent, field) = child;        \
else                        \
RB_RIGHT(parent, field) = child;    \
RB_AUGMENT(parent);                \
} else                            \
RB_ROOT(head) = child;                \
if (RB_PARENT(elm, field) == old)            \
parent = elm;                    \
(elm)->field = (old)->field;                \
if (RB_PARENT(old, field)) {                \
if (RB_LEFT(RB_PARENT(old, field), field) == old)\
RB_LEFT(RB_PARENT(old, field), field) = elm;\
else                        \
RB_RIGHT(RB_PARENT(old, field), field) = elm;\
RB_AUGMENT(RB_PARENT(old, field));        \
} else                            \
RB_ROOT(head) = elm;                \
RB_PARENT(RB_LEFT(old, field), field) = elm;        \
if (RB_RIGHT(old, field))                \
RB_PARENT(RB_RIGHT(old, field), field) = elm;    \
if (parent) {                        \
left = parent;                    \
do {                        \
RB_AUGMENT(left);            \
} while ((left = RB_PARENT(left, field)));    \
}                            \
goto color;                        \
}                                \
parent = RB_PARENT(elm, field);                    \
color = RB_COLOR(elm, field);                    \
if (child)                            \
RB_PARENT(child, field) = parent;            \
if (parent) {                            \
if (RB_LEFT(parent, field) == elm)            \
RB_LEFT(parent, field) = child;            \
else                            \
RB_RIGHT(parent, field) = child;        \
RB_AUGMENT(parent);                    \
} else                                \
RB_ROOT(head) = child;                    \
color:                                    \
if (color == RB_BLACK)                        \
name##_RB_REMOVE_COLOR(head, parent, child);        \
return (old);                            \
}                                    \
\
/* Inserts a node into the RB tree */                    \
attr struct type *                            \
name##_RB_INSERT(struct name *head, struct type *elm)            \
{                                    \
struct type *tmp;                        \
struct type *parent = NULL;                    \
int comp = 0;                            \
tmp = RB_ROOT(head);                        \
while (tmp) {                            \
parent = tmp;                        \
comp = (cmp)(elm, parent);                \
if (comp < 0)                        \
tmp = RB_LEFT(tmp, field);            \
else if (comp > 0)                    \
tmp = RB_RIGHT(tmp, field);            \
else                            \
return (tmp);                    \
}                                \
RB_SET(elm, parent, field);                    \
if (parent != NULL) {                        \
if (comp < 0)                        \
RB_LEFT(parent, field) = elm;            \
else                            \
RB_RIGHT(parent, field) = elm;            \
RB_AUGMENT(parent);                    \
} else                                \
RB_ROOT(head) = elm;                    \
name##_RB_INSERT_COLOR(head, elm);                \
return (NULL);                            \
}                                    \
\
/* Finds the node with the same key as elm */                \
attr struct type *                            \
name##_RB_FIND(struct name *head, struct type *elm)            \
{                                    \
struct type *tmp = RB_ROOT(head);                \
int comp;                            \
while (tmp) {                            \
comp = cmp(elm, tmp);                    \
if (comp < 0)                        \
tmp = RB_LEFT(tmp, field);            \
else if (comp > 0)                    \
tmp = RB_RIGHT(tmp, field);            \
else                            \
return (tmp);                    \
}                                \
return (NULL);                            \
}                                    \
\
/* Finds the first node greater than or equal to the search key */    \
attr struct type *                            \
name##_RB_NFIND(struct name *head, struct type *elm)            \
{                                    \
struct type *tmp = RB_ROOT(head);                \
struct type *res = NULL;                    \
int comp;                            \
while (tmp) {                            \
comp = cmp(elm, tmp);                    \
if (comp < 0) {                        \
res = tmp;                    \
tmp = RB_LEFT(tmp, field);            \
}                            \
else if (comp > 0)                    \
tmp = RB_RIGHT(tmp, field);            \
else                            \
return (tmp);                    \
}                                \
return (res);                            \
}                                    \
\
/* ARGSUSED */                                \
attr struct type *                            \
name##_RB_NEXT(struct type *elm)                    \
{                                    \
if (RB_RIGHT(elm, field)) {                    \
elm = RB_RIGHT(elm, field);                \
while (RB_LEFT(elm, field))                \
elm = RB_LEFT(elm, field);            \
} else {                            \
if (RB_PARENT(elm, field) &&                \
(elm == RB_LEFT(RB_PARENT(elm, field), field)))    \
elm = RB_PARENT(elm, field);            \
else {                            \
while (RB_PARENT(elm, field) &&            \
(elm == RB_RIGHT(RB_PARENT(elm, field), field)))\
elm = RB_PARENT(elm, field);        \
elm = RB_PARENT(elm, field);            \
}                            \
}                                \
return (elm);                            \
}                                    \
\
/* ARGSUSED */                                \
attr struct type *                            \
name##_RB_PREV(struct type *elm)                    \
{                                    \
if (RB_LEFT(elm, field)) {                    \
elm = RB_LEFT(elm, field);                \
while (RB_RIGHT(elm, field))                \
elm = RB_RIGHT(elm, field);            \
} else {                            \
if (RB_PARENT(elm, field) &&                \
(elm == RB_RIGHT(RB_PARENT(elm, field), field)))    \
elm = RB_PARENT(elm, field);            \
else {                            \
while (RB_PARENT(elm, field) &&            \
(elm == RB_LEFT(RB_PARENT(elm, field), field)))\
elm = RB_PARENT(elm, field);        \
elm = RB_PARENT(elm, field);            \
}                            \
}                                \
return (elm);                            \
}                                    \
\
attr struct type *                            \
name##_RB_MINMAX(struct name *head, int val)                \
{                                    \
struct type *tmp = RB_ROOT(head);                \
struct type *parent = NULL;                    \
while (tmp) {                            \
parent = tmp;                        \
if (val < 0)                        \
tmp = RB_LEFT(tmp, field);            \
else                            \
tmp = RB_RIGHT(tmp, field);            \
}                                \
return (parent);                        \
}

#define RB_NEGINF    -1
#define RB_INF    1

#define RB_INSERT(name, x, y)    name##_RB_INSERT(x, y)
#define RB_REMOVE(name, x, y)    name##_RB_REMOVE(x, y)
#define RB_FIND(name, x, y)    name##_RB_FIND(x, y)
#define RB_NFIND(name, x, y)    name##_RB_NFIND(x, y)
#define RB_NEXT(name, x, y)    name##_RB_NEXT(y)
#define RB_PREV(name, x, y)    name##_RB_PREV(y)
#define RB_MIN(name, x)        name##_RB_MINMAX(x, RB_NEGINF)
#define RB_MAX(name, x)        name##_RB_MINMAX(x, RB_INF)

#define RB_FOREACH(x, name, head)                    \
for ((x) = RB_MIN(name, head);                    \
(x) != NULL;                        \
(x) = name##_RB_NEXT(x))

#define RB_FOREACH_SAFE(x, name, head, y)                \
for ((x) = RB_MIN(name, head);                    \
((x) != NULL) && ((y) = name##_RB_NEXT(x), 1);        \
(x) = (y))

#define RB_FOREACH_REVERSE(x, name, head)                \
for ((x) = RB_MAX(name, head);                    \
(x) != NULL;                        \
(x) = name##_RB_PREV(x))

#define RB_FOREACH_REVERSE_SAFE(x, name, head, y)            \
for ((x) = RB_MAX(name, head);                    \
((x) != NULL) && ((y) = name##_RB_PREV(x), 1);        \
(x) = (y))


/*
 * Copyright (c) 2016 David Gwynne <dlg@openbsd.org>
 *
 * Permission to use, copy, modify, and distribute this software for any
 * purpose with or without fee is hereby granted, provided that the above
 * copyright notice and this permission notice appear in all copies.
 *
 * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
 * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
 * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR
 * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
 * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN
 * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF
 * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
 */

struct rb_type {
    int        (*t_compare)(const void *, const void *);
    void        (*t_augment)(void *);
    unsigned int      t_offset;    /* offset of rb_entry in type */
};

struct rb_tree {
    struct rb_entry    *rbt_root;
};

struct rb_entry {
    struct rb_entry     *rbt_parent;
    struct rb_entry     *rbt_left;
    struct rb_entry     *rbt_right;
    unsigned int      rbt_color;
};

#define RBT_HEAD(_name, _type)                        \
struct _name {                                \
struct rb_tree rbh_root;                    \
}

#define RBT_ENTRY(_type)    struct rb_entry

static inline void
_rb_init(struct rb_tree *rbt)
{
    rbt->rbt_root = NULL;
}

static inline int
_rb_empty(struct rb_tree *rbt)
{
    return (rbt->rbt_root == NULL);
}

void    *_rb_insert(const struct rb_type *, struct rb_tree *, void *);
void    *_rb_remove(const struct rb_type *, struct rb_tree *, void *);
void    *_rb_find(const struct rb_type *, struct rb_tree *, const void *);
void    *_rb_nfind(const struct rb_type *, struct rb_tree *, const void *);
void    *_rb_root(const struct rb_type *, struct rb_tree *);
void    *_rb_min(const struct rb_type *, struct rb_tree *);
void    *_rb_max(const struct rb_type *, struct rb_tree *);
void    *_rb_next(const struct rb_type *, void *);
void    *_rb_prev(const struct rb_type *, void *);
void    *_rb_left(const struct rb_type *, void *);
void    *_rb_right(const struct rb_type *, void *);
void    *_rb_parent(const struct rb_type *, void *);
void     _rb_set_left(const struct rb_type *, void *, void *);
void     _rb_set_right(const struct rb_type *, void *, void *);
void     _rb_set_parent(const struct rb_type *, void *, void *);
void     _rb_poison(const struct rb_type *, void *, unsigned long);
int     _rb_check(const struct rb_type *, void *, unsigned long);

#define RBT_INITIALIZER(_head)    { { NULL } }

#define RBT_PROTOTYPE(_name, _type, _field, _cmp)            \
extern const struct rb_type *const _name##_RBT_TYPE;            \
\
__unused static inline void                        \
_name##_RBT_INIT(struct _name *head)                    \
{                                    \
_rb_init(&head->rbh_root);                    \
}                                    \
\
__unused static inline struct _type *                    \
_name##_RBT_INSERT(struct _name *head, struct _type *elm)        \
{                                    \
return (struct _type *)_rb_insert(_name##_RBT_TYPE, &head->rbh_root, elm);    \
}                                    \
\
__unused static inline struct _type *                    \
_name##_RBT_REMOVE(struct _name *head, struct _type *elm)        \
{                                    \
return (struct _type *)_rb_remove(_name##_RBT_TYPE, &head->rbh_root, elm);    \
}                                    \
\
__unused static inline struct _type *                    \
_name##_RBT_FIND(struct _name *head, const struct _type *key)        \
{                                    \
return (struct _type *)_rb_find(_name##_RBT_TYPE, &head->rbh_root, key);    \
}                                    \
\
__unused static inline struct _type *                    \
_name##_RBT_NFIND(struct _name *head, const struct _type *key)        \
{                                    \
return (struct _type *)_rb_nfind(_name##_RBT_TYPE, &head->rbh_root, key);    \
}                                    \
\
__unused static inline struct _type *                    \
_name##_RBT_ROOT(struct _name *head)                    \
{                                    \
return (struct _type *)_rb_root(_name##_RBT_TYPE, &head->rbh_root);        \
}                                    \
\
__unused static inline int                        \
_name##_RBT_EMPTY(struct _name *head)                    \
{                                    \
return _rb_empty(&head->rbh_root);                \
}                                    \
\
__unused static inline struct _type *                    \
_name##_RBT_MIN(struct _name *head)                    \
{                                    \
return (struct _type *)_rb_min(_name##_RBT_TYPE, &head->rbh_root);        \
}                                    \
\
__unused static inline struct _type *                    \
_name##_RBT_MAX(struct _name *head)                    \
{                                    \
return (struct _type *)_rb_max(_name##_RBT_TYPE, &head->rbh_root);        \
}                                    \
\
__unused static inline struct _type *                    \
_name##_RBT_NEXT(struct _type *elm)                    \
{                                    \
return (struct _type *)_rb_next(_name##_RBT_TYPE, elm);                \
}                                    \
\
__unused static inline struct _type *                    \
_name##_RBT_PREV(struct _type *elm)                    \
{                                    \
return (struct _type *)_rb_prev(_name##_RBT_TYPE, elm);                \
}                                    \
\
__unused static inline struct _type *                    \
_name##_RBT_LEFT(struct _type *elm)                    \
{                                    \
return (struct _type *)_rb_left(_name##_RBT_TYPE, elm);                \
}                                    \
\
__unused static inline struct _type *                    \
_name##_RBT_RIGHT(struct _type *elm)                    \
{                                    \
return (struct _type *)_rb_right(_name##_RBT_TYPE, elm);            \
}                                    \
\
__unused static inline struct _type *                    \
_name##_RBT_PARENT(struct _type *elm)                    \
{                                    \
return (struct _type *)_rb_parent(_name##_RBT_TYPE, elm);            \
}                                    \
\
__unused static inline void                        \
_name##_RBT_SET_LEFT(struct _type *elm, struct _type *left)        \
{                                    \
return _rb_set_left(_name##_RBT_TYPE, elm, left);        \
}                                    \
\
__unused static inline void                        \
_name##_RBT_SET_RIGHT(struct _type *elm, struct _type *right)        \
{                                    \
return _rb_set_right(_name##_RBT_TYPE, elm, right);        \
}                                    \
\
__unused static inline void                        \
_name##_RBT_SET_PARENT(struct _type *elm, struct _type *parent)        \
{                                    \
return _rb_set_parent(_name##_RBT_TYPE, elm, parent);        \
}                                    \
\
__unused static inline void                        \
_name##_RBT_POISON(struct _type *elm, unsigned long poison)        \
{                                    \
return _rb_poison(_name##_RBT_TYPE, elm, poison);        \
}                                    \
\
__unused static inline int                        \
_name##_RBT_CHECK(struct _type *elm, unsigned long poison)        \
{                                    \
return _rb_check(_name##_RBT_TYPE, elm, poison);        \
}

#define RBT_GENERATE_INTERNAL(_name, _type, _field, _cmp, _aug)        \
static int                                \
_name##_RBT_COMPARE(const void *lptr, const void *rptr)            \
{                                    \
const struct _type *l = (struct _type *)lptr, *r = (struct _type *)rptr;            \
return _cmp(l, r);                        \
}                                    \
static const struct rb_type _name##_RBT_INFO = {            \
_name##_RBT_COMPARE,                        \
_aug,                                \
offsetof(struct _type, _field),                    \
};                                    \
const struct rb_type *const _name##_RBT_TYPE = &_name##_RBT_INFO

#define RBT_GENERATE_AUGMENT(_name, _type, _field, _cmp, _aug)        \
static void                                \
_name##_RBT_AUGMENT(void *ptr)                        \
{                                    \
struct _type *p = (struct _type *)ptr;                        \
return _aug(p);                            \
}                                    \
RBT_GENERATE_INTERNAL(_name, _type, _field, _cmp, _name##_RBT_AUGMENT)

#define RBT_GENERATE(_name, _type, _field, _cmp)            \
RBT_GENERATE_INTERNAL(_name, _type, _field, _cmp, NULL)

#define RBT_INIT(_name, _head)        _name##_RBT_INIT(_head)
#define RBT_INSERT(_name, _head, _elm)    _name##_RBT_INSERT(_head, _elm)
#define RBT_REMOVE(_name, _head, _elm)    _name##_RBT_REMOVE(_head, _elm)
#define RBT_FIND(_name, _head, _key)    _name##_RBT_FIND(_head, _key)
#define RBT_NFIND(_name, _head, _key)    _name##_RBT_NFIND(_head, _key)
#define RBT_ROOT(_name, _head)        _name##_RBT_ROOT(_head)
#define RBT_EMPTY(_name, _head)        _name##_RBT_EMPTY(_head)
#define RBT_MIN(_name, _head)        _name##_RBT_MIN(_head)
#define RBT_MAX(_name, _head)        _name##_RBT_MAX(_head)
#define RBT_NEXT(_name, _elm)        _name##_RBT_NEXT(_elm)
#define RBT_PREV(_name, _elm)        _name##_RBT_PREV(_elm)
#define RBT_LEFT(_name, _elm)        _name##_RBT_LEFT(_elm)
#define RBT_RIGHT(_name, _elm)        _name##_RBT_RIGHT(_elm)
#define RBT_PARENT(_name, _elm)        _name##_RBT_PARENT(_elm)
#define RBT_SET_LEFT(_name, _elm, _l)    _name##_RBT_SET_LEFT(_elm, _l)
#define RBT_SET_RIGHT(_name, _elm, _r)    _name##_RBT_SET_RIGHT(_elm, _r)
#define RBT_SET_PARENT(_name, _elm, _p)    _name##_RBT_SET_PARENT(_elm, _p)
#define RBT_POISON(_name, _elm, _p)    _name##_RBT_POISON(_elm, _p)
#define RBT_CHECK(_name, _elm, _p)    _name##_RBT_CHECK(_elm, _p)

#define RBT_FOREACH(_e, _name, _head)                    \
for ((_e) = RBT_MIN(_name, (_head));                \
(_e) != NULL;                        \
(_e) = RBT_NEXT(_name, (_e)))

#define RBT_FOREACH_SAFE(_e, _name, _head, _n)                \
for ((_e) = RBT_MIN(_name, (_head));                \
(_e) != NULL && ((_n) = RBT_NEXT(_name, (_e)), 1);    \
(_e) = (_n))

#define RBT_FOREACH_REVERSE(_e, _name, _head)                \
for ((_e) = RBT_MAX(_name, (_head));                \
(_e) != NULL;                        \
(_e) = RBT_PREV(_name, (_e)))

#define RBT_FOREACH_REVERSE_SAFE(_e, _name, _head, _n)            \
for ((_e) = RBT_MAX(_name, (_head));                \
(_e) != NULL && ((_n) = RBT_PREV(_name, (_e)), 1);    \
(_e) = (_n))

#endif    /* _SYS_TREE_H_ */
